Super-Kamiokande Physics III: Next Steps: Filling in the Matrix
The Neutrino Neutrino Oscillations Assume are MASS STATES FLAVOR STATES superpositions | n > of | n > f m weakly interacting unitary mixing matrix
N |f >=∑ Ufi |i > i=1
If mixing matrix is not diagonal, get flavor oscillations as neutrinos propagate Simple two-flavor case
|f >= cos|1 >sin|2 >
|g >=−sin|1 >cos|2 > Propagate a distance L: 2 −iEi t −imi L/2p |i ( t )>=e |i (0)>~e |i (0)> Probability of detecting flavor g at L:
2 E in GeV 2 2 1.27m L L in km 2 P(f g )=sin 2sin E Dm2 in eV2 2 2 1.27m L Parameters of nature to measure: q, Dm2=m 2-m 2 P( )=s1in2 2sin f g E More generally, for 3 flavors: Maki- Ue1 Ue2 Ue3 e 1 Nakagawa- U U U = 1 2 3 2 Sakata (MNS) U U U matrix 1 2 3 3
2
* * 2 1.27 mij L P(f g )=fg−4∑ Re(Ufi Ugi Ufj Ugj )sin ji E 2 * * 2.54 mij L ±2∑ Im(Ufi Ugi Ufj Ugj )sin ji E Frequently, can use 2-flavor approximation e.g. if Dm 2 >> Dm 2 ij jk 2 ● 3 flavors 2 independent Dm NNotes: ij ● sterile n with no weak interactions? The Three Signals in Parameter Space to be tested (for now, LSND e assume LSND was wrong)
Atmospheric x n's confirmed by K2K Solar and e x multiply reactor confirmed n's "Standard" 3-flavor picture: Absolute mass Parameters: 2 Dm2, 3 angles, d , (2 d ) scale anything CP M N less than about 2 eV |f >=∑ Ufi |i > i=1 i MNS 1 0 0 C13 0 S13 e C12 S12 0 mixing U= 0 C23 S23 0 1 0 −S12 C12 0 matrix 0 −S C −S ei 0 C 0 0 1 23 23 13 13 atmospheric ??? solar solar ??? atmospheric 3 3 3 3 t t t m t e 1 1 1 1 m m m e e e 2 2 2 2 What we really want to know: Why is there more matter than antimatter in the universe? BARYOGENESIS (or LEPTOGENESIS): the process by which an excess of matter (vs antimatter) accumulated
This may have a lot to do with neutrinos; so before we can answer these questions, we need to understand the properties of neutrinos Remaining Neutrino Questions (that can be answered by oscillation experiments) What is the mass hierarchy? "Normal" hierarchy "Inverted" hierarchy m t 2 e m t 2 Dm { Dm 12 e m t 23 (atm.) { or Dm 2 2 m t Dm { e 23 { 12 e m t m t (solar) What is U ? Is it non-zero? e3 Is 2-3 mixing maximal? Do neutrinos and antineutrinos behave differently? (CP violation) The first question that can be answered: U : look for small n appearance e3 e in a n beam m n n m m,t n atmospheric-like e wiggling
For Dm 2 >> Dm 2 and E ~ LDm 2 (in vacuum): 23 12 n 23 P(n n ) = sin22q sin2q sin2(Dm2 L/4E) m e 13 23 23 small modulation ~ 1/4 Hard to measure... it's a small modulation! Need good statistics, clean sample The Next Step: Long Baseline Low Energy (~ GeV) Off Axis Beam
● precision 2-3 measurements ● search for non-zero q 13 Why off-axis? 2-body pion decay kinematics
Off-axis, neutrino energy becomes relatively independent of p energy
Barenboim et al. Off-Axis Neutrino Although get Beams some reduction in flux, get more sharply peaked energies
Good for OA2° OA0° background reduction and OA2.5° oscillation OA3° fits off-axis Future Off-Axis Beam Projects 2009+ Aim for: ~1% precision on 2-3 mixing, factor of ~10-20 for U e3 T2K: "Tokai to Kamioka" NOnA at NuMi
Existing detector: Super-K Existing beam: NuMi 295 km, <1 GeV 0.75 MW beam 750 km, few GeV beam Water Cherenkov, Scintillator, 2.5 deg. off axis sites under discussion T2K ("Tokai to Kamioka") 2o off-axis Near + 2 km detectors, Super-K refurbished by 2006
Start 2009
Beam neutrino energy tuned to oscillation minimum J-PARC beamline under construction now
nn beam-line decay volume
J-PARC Beamline Construction, Jan 2004 T2K Detectors p p off-axis n
on-axis
0m 140m 280m 2 km 295 km 1. Near detector at 280 m: fine-grained tracker 2. Intermediate detector at 2 km Water Cherenkov + fine-grain tracker (LAr) + muon ranger Beam spectrum looks more like beam at SK cancel systematics 3. Super-K III at 295 km, fully refurbished Summary Why is there more matter than antimatter? Before we can answer this question, we need to know everything about neutrinos... Before we can know if neutrinos and antineutrinos behave differently, we need to know if q is non-zero 13
i MNS 1 0 0 C13 0 S13 e C12 S12 0 mixing U= 0 C23 S23 0 1 0 −S12 C12 0 matrix 0 −S C S ei 0 C 0 0 1 23 23− 13 13 solar atmospheric ??? Experimental signature of U : e3 look for small n appearance in a n beam e m This is what we're after, with T2K off-axis beam